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Properties of Matrix Multiplication

For any matrices A, B, and C for which the matrix product is defined and any scalar k, the following properties are true.

(AB)C = A(BC)

Associative Property of Multiplication

k(AB) = (kA)B= A(kB)

Associative Property of Scalar Multiplication

Left Distributive Property

C(A+B) = CA + CB

Right Distributive Property

(A+B)C = AC + BC

identity matrix

diagonal matrix with ones in the leading diagonal and zeros in the other positions.

inverse matrix

The multiplicative inverse of a square matrix is called its inverse matrix.